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Surface Approximation by Means of Gaussian Process Latent Variable Models and Line Element Geometry

Author

Listed:
  • Ivan De Boi

    (Research Group InViLab, Department Electromechanics, Faculty of Applied Engineering, University of Antwerp, B 2020 Antwerp, Belgium)

  • Carl Henrik Ek

    (Department of Computer Science and Technology University of Cambridge, Cambridge CB3 0FD, UK)

  • Rudi Penne

    (Research Group InViLab, Department Electromechanics, Faculty of Applied Engineering, University of Antwerp, B 2020 Antwerp, Belgium)

Abstract

The close relation between spatial kinematics and line geometry has been proven to be fruitful in surface detection and reconstruction. However, methods based on this approach are limited to simple geometric shapes that can be formulated as a linear subspace of line or line element space. The core of this approach is a principal component formulation to find a best-fit approximant to a possibly noisy or impartial surface given as an unordered set of points or point cloud. We expand on this by introducing the Gaussian process latent variable model, a probabilistic non-linear non-parametric dimensionality reduction approach following the Bayesian paradigm. This allows us to find structure in a lower dimensional latent space for the surfaces of interest. We show how this can be applied in surface approximation and unsupervised segmentation to the surfaces mentioned above and demonstrate its benefits on surfaces that deviate from these. Experiments are conducted on synthetic and real-world objects.

Suggested Citation

  • Ivan De Boi & Carl Henrik Ek & Rudi Penne, 2023. "Surface Approximation by Means of Gaussian Process Latent Variable Models and Line Element Geometry," Mathematics, MDPI, vol. 11(2), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:380-:d:1032001
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    References listed on IDEAS

    as
    1. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
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    Cited by:

    1. Snezhana Gocheva-Ilieva & Atanas Ivanov & Hristina Kulina, 2023. "Special Issue “Statistical Data Modeling and Machine Learning with Applications II”," Mathematics, MDPI, vol. 11(12), pages 1-4, June.

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